Problem: Simplify the following expression: $\sqrt{117} + \sqrt{52}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{117} + \sqrt{52}$ $= \sqrt{9 \cdot 13} + \sqrt{4 \cdot 13}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{13} + \sqrt{4} \cdot \sqrt{13}$ $= 3\sqrt{13} + 2\sqrt{13}$ Finally, simplify by combining the terms. $= ( 3 + 2 )\sqrt{13} = 5\sqrt{13}$